Hamiltonian dynamics in symplectic phase space and Nambu’s formulation of mechanics

Abstract

Starting from the formulation of the Hamiltonian dynamics in phase spaces with a symplectic structure, we show that it is possible to formulate the mechanics recently proposed by Nambu by means of a mapping from the even-dimensional Hamiltonian phase space to a ’’phase space’’ which displays all properties of Nambu’s theory. The difficulties concerning the process of quantization of Nambu’s theory can be presently discussed at classical level by means of a suitable interpretation of the meaning of the several Hamiltonians of the theory. Some examples are given.